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WINTER 2014 Regularity and linearity defect of modules over local rings
Rasoul Ahangari Maleki, Maria Evelina Rossi
J. Commut. Algebra 6(4): 485-504 (WINTER 2014). DOI: 10.1216/JCA-2014-6-4-485

Abstract

Given a finitely generated module $M$ over a commutative local ring (or a standard graded $k$-algebra) $(R,\m,k)$, we detect its complexity in terms of numerical invariants coming from suitable $\m$-stable filtrations $\mathbb{M}$ on $M.$ We study the Castelnuovo-Mumford regularity of $gr_{\mathbb{M}}(M) $ and the linearity defect of $M, $ denoted $\ld_R(M), $ through a deep investigation based on the theory of standard bases. If $M$ is a graded $R$-module, then $\reg_R(gr_{\mathbb{M}}(M)) \lt \infty $ implies $\reg_R(M)\lt \infty$ and the converse holds provided $M$ is of homogenous type. An analogous result can be proved in the local case in terms of the linearity defect. Motivated by a positive answer in the graded case, we present for local rings a partial answer to a question raised by Herzog and Iyengar of whether $\ld_R(k)\lt \infty$ implies $R$ is Koszul.

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Rasoul Ahangari Maleki. Maria Evelina Rossi. "Regularity and linearity defect of modules over local rings." J. Commut. Algebra 6 (4) 485 - 504, WINTER 2014. https://doi.org/10.1216/JCA-2014-6-4-485

Information

Published: WINTER 2014
First available in Project Euclid: 5 January 2015

zbMATH: 1321.13004
MathSciNet: MR3294859
Digital Object Identifier: 10.1216/JCA-2014-6-4-485

Subjects:
Primary: 13D07, 16W50
Secondary: 16S37, 16W70

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

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Vol.6 • No. 4 • WINTER 2014
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